Table 2 Summary of included studies

Caforio et al. (2022) [33]

Aortic stiffening, COA, aging

OL

3D EM LV (MRI)

0D valve dynamics [93]

1D upper thoracic aorta; 116 SA + 3-element WK

Patient-specific data (MRI and invasive BP)

MRI clinical data under baseline conditions

Arterial stiffening increased ES volume with ED volume unaltered, resulting in a drop in SV. Increased aortic stiffness due to stenosis or aging with increased SVR caused increased peak pressure, changes in pressure profile, and a drop in SV due to a rise in ES volume

Laubscher et al. (2022) [47]

AS

CL

0D TVE

0D (M1: diode; M2: pressure loss [147]; M3: valve pressure loss and motion)

0D systemic and pulmonary circulation

Population-averaged data (literature-derived)

Typical human physiological hemodynamic parameters

The proposed M3 valve model predicted higher pressure drops at severe AS than the M1 and M2 models from literature

Regazzoni et al. (2022) [48]

HTN

CL

3D EM LV + 0D TVE LA, RA, RV

0D nonideal diode

0D systemic and pulmonary circulation

Generic data (literature-derived)

Not mentioned

Atrial contractility affected preload and SV positively. Increased arterial resistance raised AV opening pressure and maximal LV pressure (hypertensive effect). Increased myocardial contractility raised maximal LV pressure and SV

Wisneski et al. (2022) [50]

low flow low gradient AS

CL

3D FE LV (CT)

0D MV and AV

0D systemic and pulmonary circulation

Patient-specific data (echo and catheterization)

Patient clinical parameters

Contrary to idealized LV geometry and normal ventricular function, a patient-specific LV model with low flow, low gradient AS revealed a quantifiable reduction in LV stress

Zuo et al. (2022) [52]

Hypertensive myocardial hypertrophy

CL

3D CFD LV (as BC); 0D TVE LV, RV, LA

0D (diode and resistor)

0D resistance−inductance−capacitance systemic and pulmonary circulation

Generic data (literature-derived [148])

Echo measurements and MRI data on MV and AV

Myocardial hypertrophy due to HTN affected flow domain, leading to abnormal vortex distribution, higher energy loss, lower blood flow velocity, and low cardiac EF. In comparison, the energy loss and velocity distribution of HTN normal LV group were like the normal LV control group, but with slightly higher characteristic parameter values

Sadeghi et al. (2022) [49]

COA; mixed valvular diseases

CL

0D TVE LA, LV

0D MV and AV (net pressure gradient)

3D CFD thoracic aorta (CT) + 0D COA, systemic and pulmonary circulation

Patient-specific data (Doppler echo and sphygmomanometer)

Doppler echo, cardiac catheterization and 4D flow MRI data

Coexistent AR and MR with COA changed downstream velocity and created turbulence, leading to disease progression at the COA region

Manganotti et al. (2021) [34]

Aging

OL

0D (Hill-Maxwell)

0D (diode and resistor)

1D upper thoracic aorta + 3-element WK

Generic data (literature-derived [149])

Not mentioned

Aging was associated with higher systolic peak, lower diastolic BP, and a slightly increased wave propagation speed (anticipated dicrotic notch). Coupled model yielded more physiological pressure curve (trend towards merging of pressure systolic peak and dicrotic peak). Uncoupled aortic model in aging case showed nonphysiological double reflection

Pagoulatou et al. (2021) [35]

LVR, HTN

OL

0D TVE LV

0D

1D 103 SA + 3-element WK

Generic data (literature-derived)

Applanation tonometry, phase-contrast MRI and echo data

Reducing proximal aortic compliance acutely increased aortic systolic BP and PP, leading to HTN, which is partially alleviated after LV remodeling. Banding increased the forward wave amplitude, which further increases PP, and LV remodeling caused the forward pressure wave to alter its shape, resulting in a distinct upstroke and an earlier peak. The primary factor driving the transformation of the pressure waveform from an old to a young phenotype was identified as LV remodeling

Pagoulatou et al. (2021) [36]

Cardiac inotropy

OL

0D TVE LV

0D

1D 103 SA + 3-element WK

Generic data (literature-derived)

Applanation tonometry, phase-contrast MRI and echo data

AIx, based on the pressure waveform, did not exclusively reflect arterial properties, as cardiac contractility also plays a crucial role in determining central AIx

Cosentino et al. (2020) [37]

ATAA, AS

OL

0D

–

3D FSI aorta (CTA) + 3-element WK

Patient-specific data (clinical and echo data)

Echo data on AV

LV work increased with AS severity, with post-stenotic variables (including WSS) markedly increasing, particularly for severe AS models. Higher WSS and maximum principal stress of ATAA wall were associated with more severe LV dysfunction indicated by Zva

Wisneski et al. (2020) [51]

AS

CL

3D FE

–

0D systemic and pulmonary circulation

Generic data (literature-derived)

Tagged MRI data

Global LV peak systolic myofiber stress increased progressively with AS severity, while ED stress remained relatively constant across all conditions

Heusinkveld et al. (2019) [53]

Cardiac inotropy, vascular aging, cardiac and vascular tissue changes

CL

0D (modified Hill)

–

1D TL arterial and venous tree + 0D peripheral circulation

Generic data (literature-derived [150])

Applanation tonometry data

Both LV contraction velocity and increased arterial stiffness affected AIx. However, a rise in AIx did not necessarily correspond to a rise in LV SW. Wave reflection magnitude, determined by considering both pressure and flow, was also a factor in determining LV SW

Syomin et al. (2019) [65]

AS, AR, MS, MR

CL

2D axisymmetric FE LV + 0D atria and RV

0D (diode, resistor, inductor, capacitor)

0D systemic and pulmonary circulation

Generic data (typical values)

Published clinical data

AS: Reduced AV maximal orifice area resulted in a rise in the mean and maximal pressure difference between the LV and aorta, along with a decrease in LV ED and ES volumes, SV, and EF

MS: LV ED volume and SV decreased significantly at a constant blood volume

AR and MR: Regurgitant volume and fraction increased with the maximal orifice area of valve

Gul et al. (2019) [38]

Aortic stenosis and aneurysm

OL

0D TVE LV

0D MV and AV (diode)

0D 122 systemic circulation

Generic population data (literature-derived)

Not mentioned

In the presence of aortic stenoses (aneurysms), node 34 (33) had a greater impact on pressure and flow than node 33 (34). Sensitivity of pressure and flow in the systemic circulation to stenoses and aneurysms increased with higher HRs

Shavik et al. (2018) [64]

Aortic remodeling (wall thickening and stiffening), LV stiffening

CL

3D FE half prolate ellipsoid LV

0D MV and AV

3D FE idealized aorta + 0D systemic circulation

Generic data (literature-derived)

Population-averaged in vivo data from different literature

Increasing aorta wall thickness caused a lower LV EF, higher peak LV systolic BP, and leftward shift in the aorta pressure-diameter relationship with smaller diameter at ED and ES. Elevated collagen mass increased peak systolic BP but reduced LV EF. Decreasing LV contractility and increasing passive stiffness lowered LV EF, aortic systolic BP, PP, and peak stress

Liang et al. (2018) [56]

HTN, arterial stiffening

CL

0D TVE

–

1D 55 SA + ST + 0D pulmonary circulation, capillaries and veins

Population-averaged data (literature-derived)

Normal human data under physiological condition

BP and flow pulsatility indices in both large arteries and microcirculation were mainly determined by heart period, arteriolar radius, and central arterial stiffness. To fully account for the pressure-lowering effects in the aorta, central arterial stiffness must be reduced simultaneously with the structural normalization of distal vessels

Pagoulatou et al. (2017) [39]

Aging

OL

0D TVE LV

0D

1D 103 SA + 3-element WK

Population-averaged data (literature-derived)

Published data from large-scale clinical studies [151, 152]

The forward wave was the main cause of central and peripheral systolic BP and PP increase with age due to a stiffening proximal aorta that augmented it. AIx steeply increased in young adults but declined after 60 years

Maksuti et al. (2016) [59]

Aging

CL

0D TVE LV

0D (diode)

0D 4-element WK SA

Generic data

Population data (Framingham Heart Study)

Arterial and cardiac factors both contributed to age-related changes in BP. Arterial changes led to a rise in systolic BP, which triggered cardiac remodeling, further increasing systolic BP and mitigating the decrease in diastolic BP

Chen et al. (2016) [40]

Arterial stiffening, rarefaction, LVH, inotropy

OL

3D FSI (MRI)

3D passive AV

1D 24 SA + ST

Subject-specific and generic data (MRI, literature-derived)

Published experimental data (healthy subjects)

Arterial stiffening and rarefaction led to higher BP, LV active tension, but decreased SV. LV stiffening caused severely impaired pump function, reducing active tension, SV, and BP. Elevated contractility could maintain a higher SV but raised circulation pressure. Isolated systemic circulation model overestimated peak pressure (up to 7%) and flow rate (up to 20%) compared to a coupled model

Inuzuka et al. (2016) [55]

HF progression with chronic mitral regurgitation

CL

0D modified TVE

–

0D systemic and pulmonary circulation (modified 3-element WK)

Generic data (literature-derived [153])

Echo data

Increase in HR decreased EF and increased MPI. Ees reduction also decreased EF and increased MPI. Volume overload and ventricular stiffening decreased MPI. Higher SVR increased afterload, leading to decreased EF and increased MPI, while afterload decrease due to reduced arterial compliance decreased both. These MPI characteristics led to paradoxical MPI improvement during chronic HF disease progression in a simulation of MR

Palau-Caballero et al. (2016) [60]

AR, LV and aortic stiffness

CL

0D

0D

0D aorta, pulmonary and peripheral circulation

Generic data (literature-derived)

Echo data across AV from AR patients

AR severity scores (regurgitant EOA, regurgitant fraction, pressure half time) poorly reflected mean left atrial pressure when variations in tissue properties (LV and/or aortic stiffness) were present

Guala et al. (2015) [41]

Aging, aortic stiffening and remodeling

OL

0D TVE LV

0D AV dynamics

1D SA + 3-element WK

Generic data (literature-derived)

Arterial tonometry

Aging-induced aortic stiffening amplified the first pressure pulsed at the VA interface, while remodeling suppressed it. Though stiffening tended to decline reflection coefficients at network bifurcations, the substantial growth induced by remodeling prevailed, raising the overall amount of reflection. Aortic remodeling undermined the protective wave-trapping mechanism on reflected pressure waves, whereas stiffening improved it. Both aortic stiffening and remodeling had a compensatory effect on PP amplification, with the former reducing it, and the latter increasing it. Together, they helped restrain the LV work growth associated with aging

Keshavarz-Motamed et al. (2014) [42]

AS

OL

0D TVE

0D AV (diode, variable resistor, inductor)

0D systemic circulation

Population-averaged data (transthoracic Doppler echo and MRI)

MRI data (healthy subject and AS patient)

The proposed normalized LV SW correlated well with Zva, a validated index of global hemodynamic load, and was less flow-dependent than Zva

Veress et al. (2013) [66]

HTN

CL

3D FE LV (as BC); 0D TVE LA, LV

–

0D WK systemic circulation

Generic data (literature-derived)

Not mentioned

Mild and moderate HTN caused an increase in cardiac output and SV compared to normotension. Even mild HTN could significantly increase total LV wall stress. A moderate increase in afterload led to a substantial increase in circulatory work values

Blanco et al. (2013) [54]

AR, cerebral aneurysm

CL

0D TVE

0D (nonideal diode)

1D 128 SA + 3-element WK peripheral circulation + 0D resistance-inductance-capacitance venous and pulmonary circulation (3D CFD cerebral aneurysm)

Generic data (literature-derived)

Patient-specific records from literature

The hemodynamic response to changes in AV pathological condition was sensitive. WSS and OSI maps remained stable, except in acute conditions. WSS index decreased with worsening of pathology, while OSI increased. Mean residence time of particles decreased with increasing severity of insufficiency

Keshavarz-Motamed et al. (2011) [43]

AS (no, mild, moderate, severe AS), COA

OL

0D TVE LV

0D AV (diode, variable resistor, inductor)

0D COA and systemic circulation

Generic data (typical physiological values)

MRI data through COA (patient with coexistent COA and AS)

AS severity increased LV peak pressure, lengthened ejection time. and delayed peak transvalvular flow rate during ejection. COA severity reduced the proportion of total flow rate crossing it. AS and COA severity increased LV SW. LV SW decreased with increasing AV EOA (AV replacement) and decreasing COA area (COA repair)

Liang et al. (2009) [58]

AS, arterial stenoses

CL

0D TVE

0D pressure−flow relationship

1D 55 SA + 0D peripheral and pulmonary circulation

Generic data (literature-derived)

Echo data around left heart [154]

Global hemodynamic effects of stenoses were location-dependent, with AS and aortic stenosis having pronounced hemodynamic changes. AS notably impacted ventricular dynamics and aortic flow, while aortic stenosis had moderate effects with renal and femoral arterial stenoses had minimal impact

Liang et al. (2009) [57]

Aging

CL

0D TVE

–

1D 55 SA + 0D peripheral and pulmonary circulation

Generic data (literature-derived)

Arterial tonometry and SphygmoCor [155]

Isolated arterial stiffening due to aging caused large increases in ES pressure and PV area, moderate decreases in SV and EF, and minor changes in SW and LV power. Coupled VA stiffening during aging preserved SV and EF and increased ES pressure, SW, PV area, and peak LV power compared to isolated arterial stiffening. Arterial stiffening led to increased aortic systolic HTN and PP in old age due to increased aortic characteristic impedance and premature wave reflection. Aortic dilatation could partly counteract these negative effects

Garcia et al. (2007) [44]

AS, systemic HTN, LVH

OL

0D LV

0D pressure-flow relationship AV

0D 3-element WK SA

Generic data (typical physiological values)

Catheterization data (patient underwent AV replacement)

Systemic HTN strongly affected LVH development in AS patients. Mild-to-moderate AS had a lesser impact on LV wall volume than HTN, while severe AS significantly increased wall volume and impacted LVH

Formaggia et al. (2006) [45]

Aging, atherosclerosis

OL

0D TVE LV

AV (closed/opened)

1D 55 SA + 3-element WK

Generic data (literature-derived [95])

Not mentioned

Uncoupled model (vessel) underestimated reflections in the pathological case; the coupled model (heart-vessel) showed greater sensitivity to variations in arterial stiffness. In young adults, waves moved slowly with late arrival of reflections in diastole, while in older individuals wave speed increased and reflections returned in systole. Arterial obstruction had minimal impact on flow and pressure wave contours of the proximal aorta, but the diseased artery markedly altered the contours

Segers et al. (2002) [61]

AR

CL

0D TVE LV

0D AV (resistor) and MV (resistor and diode)

0D 4-element WK SA

Population-averaged data (cardiac catheterization data from [156])

Catheterization data

Aortic leak severity determined Ea through leak resistance. AV repair would increase Ea assuming all other parameters are constant. LV pump efficiency (SW/PV area) was lower than the theoretical predicted value for a given Ea/Ees, except for simulations with intact AV

Sugimachi et al. (2001) [46]

Arteriosclerosis

OL

0D TVE LV

0D AV (diode)

0D SA

Population-averaged data (cardiac catheterization data from [120])

Not mentioned

Increased arterial reflections due to arterial sclerosis had a mild detrimental effect on LV pump function compared to increased peripheral resistance, mainly due to arterial stiffness rather than increased high-frequency reflections

Segers et al. (2000) [63]

Cardiac and arterial hypertrophy and remodeling

CL

0D TVE LV

0D MV and AV (diode)

0D 4-element WK SA

Population-averaged data (sphygmanometer and echo, literature derived [157])

Sphygmo-manometer and echo data

Vascular stiffening raised PP but not systolic BP alone. Arterial remodeling caused HTN only when combined with increased peripheral resistance. In normal LV, concentric remodeling, concentric hypertrophy, and eccentric hypertrophy with HTN, the cardiac contribution to systolic BP increase was 55%, 21%, 65%, and 108% respectively with remaining arterial changes

Segers et al. (2000) [62]

Aging, HTN, LVH

CL

0D TVE LV

0D MV (resistor)

0D 4-element WK SA

Population-averaged data (literature derived)

Catheterization data

Concentric LVH was an adaptation to increased afterload, where LV wall thickness increased to normalize peak systolic wall stress, and increased preload filled to compensate for impaired diastolic filling and normalized ED wall stress